On the one hand, mathematics draws inspiration from everyday life and has the ambition to model it through a precise logical system, while on the other, it contributes new, sometimes very abstract ideas which expand our imagination and broaden our understanding of the surrounding reality. This is clearly illustrated when we scrutinize various mathematical concepts centered around the notion of “boundary.”

The objective of the article involves presenting innovative approach to the assessment of structural reliability analysis. The primary research method was the First Order Reliability Method (FORM). The Hasofer–Lind reliability index in conjunction with transformation method in the FORM was adopted as the reliability measure. The implicit limit state functions were used in the analysis. The formulation of the random variables functions were created in the Matlab software by means of neural networks (NNs). The reliability analysis was conducted in Comrel module of Strurel computing environment. In the proposed approach, Hybrid FORM method (HF) used the concept in which NNs replaced the polynomial limit state functions obtained from FEM (Finite Elements Method) for chosen limit parameters of structure work. The module Comrel referenced Matlab files containing limit state functions. In the reliability analysis of structure, uncertain and uncorrelated parameters, such us base wind speed, characteristic snow load, elasticity modulus for steel and yield point steel are represented by random variables. The criterion of structural failure was expressed by four limit state functions – two related to the ultimate limit state and two related to the serviceability limit state. Using module Comrel values of the reliability index with the FORM method were determined. Additionally, the sensitivity of the reliability index to random variables and graph of partial safety factors were described. Replacing the FEM program by NNs significantly reduces the time needed to solve the task. Moreover, it enables the parallel formulation of many limit functions without extending the computation time.